Interpretable Dynamics Learning with Kolmogorov–Arnold Networks

Abstract

Learned dynamics models are central to model-based control, but the Multilayer Perceptrons (MLPs) commonly used for this purpose are opaque: it is difficult to determine which inputs drive a prediction or whether the model has captured physically meaningful structure. Kolmogorov–Arnold Networks (KANs) place learnable univariate functions on the edges of the network and can, in principle, be sparsified, pruned, and converted into closed-form expressions, which makes them a candidate for interpretable dynamics learning. The evidence for this, however, comes largely from low-dimensional scientific regression, and it is unclear how far it extends to higher-dimensional, contact-rich robotic systems.

This thesis evaluates KANs as interpretable transition-dynamics models for continuous control, using parameter-matched MLPs as the reference architecture. A single offline pipeline is applied to three Gymnasium environments of increasing complexity: Pendulum-v1, Reacher-v5, and HalfCheetah-v5. In each environment, Soft Actor-Critic (SAC) behavior policies are trained and checkpointed at several skill levels, offline transition datasets are collected from multiple behavior distributions, and dynamics models are trained to predict discrete-time state increments. The models are compared on one-step prediction accuracy, open-loop rollout behavior, and interpretability through sparsification, pruning, and automatic symbolic extraction, with the headline comparisons repeated over three random seeds.

The accuracy comparison depends on the environment rather than favoring either architecture uniformly: the two are equivalent on Pendulum-v1, the KAN matches the MLP in same-distribution accuracy while generalizing better across behavior distributions on Reacher-v5, and the MLP is the more accurate one-step predictor on the contact-rich HalfCheetah-v5, where the KAN instead shows a long-horizon rollout-stability trend. One-step error and rollout behavior produce different model rankings across environments. The most reproducible finding concerns the data rather than the models: across all environments, architectures, and seeds, the composition of the training data governs cross-distribution generalization more strongly than the choice of architecture. Applying one interpretability protocol across the three environments locates a boundary within the studied progression: compact symbolic recovery succeeds on Pendulum-v1, where the recovered angular-velocity dynamics match the analytic environment coefficients, succeeds only partially on Reacher-v5, and fails under the same criterion on HalfCheetah-v5. Because every symbolic model is re-evaluated on the same held-out data as its neural counterpart, this boundary is a measured one.